Hello Rodger and Welcome to the Forum:
Some long threaded rods will anchor the walls permanently. Use 2 in each wall, place them near a stud and countersink the top to leave a smooth surface for the sheetrock; connect the other end to a 2" X 6" block under the floor joists. The normal nailing should also be done but the 4 rods will make the permanent anchor for the 2 walls. Be sure to use moisture resistant wall board or, even better, use the cementious wall board. I wish you the best on your project and we would appreciate pictures of your progress.
Glenn

The absolute best way to anchor a knee wall is to cut the floor for a post to pass through. The post should be flush with the bottom of the joists.Then a 2x under the joists and another 2x in between the joists and fastened solid to the joists and the post. Tight fit is the key here to reduce movement.

The 2x under the joists should attach to at least 3 floor joists. In the case of an upstairs knee wall, there should be bridging between the next joist spaces on each side of the space where the post passes through the floor. This means ceiling work will be necessary. Once again, tight fit is the key to less wiggle.

The post can be 2 2x4s or a pair of 2x6s nailed together with 1/2" plywood ripped and fitted between them. Trace the end of the post right on the floor and cut to the inside of the lines.

Another 2x fastened against the bottom of the floor and attached to the post at the top will make up some for a loose cut. Tight fit is best.

Square tube steel.
Fast food places have this same thing to hold up tables and benches.
A 3" hole in the floor, a piece of 2"x2" steel square tubing.
The tubing can run as high as the knee wall framing.
Anchor it in the floor with cement mix or an epoxy patch mix.
Seal the bottom of the hole, seal the top of the tube..
or even better, fill it with cement after you get it bolted to the framing.
It won't move.